Anika says it well. I do not personally think it is cheating but I'd say this about it. leaving out the debate about wheter Porn is cheating or not, the issue at hand is that if a partner is hurt by it, it is worth giving up or working out with the partner. It matters very little whether it's drugs, porn, or anything for that matter, if it hurts your SO you need to make a choice between keeping that vice or keeping the SO. I think no matter how you look it, if you love someone you're willing to sacrifice for them.
I know how strong the pull of porn can be, it's not an uncommon thing but trust me, it's not impossible to get over. If she hasn't actually moved on and you're truly in love and committed to this woman, then you gotta find help, it's out there. Get rid of the porn for her sake. Again, technically it's not necessarily cheating but in your case it's not worth hanging onto.
The thing about porn is that it is a drug, one that heightens certain activity in the brain and combined with masturbation it can become addictive if the person is prone to addiction of any kind. It sounds to me as if you truly are addicted, since as you say you can leave it alone but not forever and the urge returns after some time. The ease at which you can find porn on the internet for free doesn't make your struggle any easier to overcome either. This is a serious addiction, not in the sense that I'm saying its wrong or bad so much as It's serious in that it's a very strong addiction that you should probably not try to overcome on your own. You need help with getting over it and it's gonna take time. I hope that you do so and I hope that with your serious efforts, she'll give you some time to change this.
once again, I don't condemn anyone for looking at porn at all, just in this case, I think it needs to go in order to restore the relationship.
here are some links that might help. Look at them with your partner if she's willing to.
http://www.sexualrecovery.com/pornography-addiction.php
http://www.feedtherightwolf.org/
http://www.no-porn.com/breaking.html
If you're a Christian, this could be helpful:
http://www.settingcaptivesfree.com/